2) Suppose that the total profit P(x) (in dollars) to manufacture a quantity x of pumpkin spice soda (in thousands of gallons) is given by the function P(x) = -x3 + 39x2 - 144x - 1313. {12 pts} a) What is a reasonable domain for this function? b) Determine the interval(s) on which P(x) is increasing and the interval(s) on which P(x) is decreasing